{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:WTPC5YYKPQX5ADP3ANYRRB2DHQ","short_pith_number":"pith:WTPC5YYK","schema_version":"1.0","canonical_sha256":"b4de2ee30a7c2fd00dfb03711887433c0356364f433546492891e0095fdfff5f","source":{"kind":"arxiv","id":"1602.06780","version":2},"attestation_state":"computed","paper":{"title":"Packing minor-closed families of graphs into complete graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Mathias Schacht, Silvia Messuti, Vojt\\v{e}ch R\\\"odl","submitted_at":"2016-02-22T14:10:31Z","abstract_excerpt":"Motivated by a conjecture of Gy\\'arf\\'as, recently B\\\"ottcher, Hladk\\'y, Piguet, and Taraz showed that every collection $T_1,\\dots,T_t$ of trees on $n$ vertices with $\\sum_{i=1}^te(T_i)\\leq \\binom{n}{2}$ and with bounded maximum degree, can be packed into the complete graph on $(1+o(1))n$ vertices. We generalise this result where we relax the restriction of packing families of trees to families of graphs of any given non-trivial minor-closed class of graphs."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1602.06780","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-02-22T14:10:31Z","cross_cats_sorted":[],"title_canon_sha256":"c114909827595d7efa9d02fdac161176a6ea73ecc93d3318493f93bd718ed2cb","abstract_canon_sha256":"b2ee5f2c2758700711a2ede489ef717bea2b640f6b90ccb77a96d5891d66294c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:54.474788Z","signature_b64":"6MlrnbPR6yA7oX4r7gezUaGxxLc8kIwATrvEtwGoDaUdRx0wB7pmbOQvy03x4JOqqRRpm6j6D9ZHSuRcVx7CDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b4de2ee30a7c2fd00dfb03711887433c0356364f433546492891e0095fdfff5f","last_reissued_at":"2026-05-18T01:16:54.473860Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:54.473860Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Packing minor-closed families of graphs into complete graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Mathias Schacht, Silvia Messuti, Vojt\\v{e}ch R\\\"odl","submitted_at":"2016-02-22T14:10:31Z","abstract_excerpt":"Motivated by a conjecture of Gy\\'arf\\'as, recently B\\\"ottcher, Hladk\\'y, Piguet, and Taraz showed that every collection $T_1,\\dots,T_t$ of trees on $n$ vertices with $\\sum_{i=1}^te(T_i)\\leq \\binom{n}{2}$ and with bounded maximum degree, can be packed into the complete graph on $(1+o(1))n$ vertices. We generalise this result where we relax the restriction of packing families of trees to families of graphs of any given non-trivial minor-closed class of graphs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.06780","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1602.06780","created_at":"2026-05-18T01:16:54.473987+00:00"},{"alias_kind":"arxiv_version","alias_value":"1602.06780v2","created_at":"2026-05-18T01:16:54.473987+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.06780","created_at":"2026-05-18T01:16:54.473987+00:00"},{"alias_kind":"pith_short_12","alias_value":"WTPC5YYKPQX5","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_16","alias_value":"WTPC5YYKPQX5ADP3","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_8","alias_value":"WTPC5YYK","created_at":"2026-05-18T12:30:51.357362+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WTPC5YYKPQX5ADP3ANYRRB2DHQ","json":"https://pith.science/pith/WTPC5YYKPQX5ADP3ANYRRB2DHQ.json","graph_json":"https://pith.science/api/pith-number/WTPC5YYKPQX5ADP3ANYRRB2DHQ/graph.json","events_json":"https://pith.science/api/pith-number/WTPC5YYKPQX5ADP3ANYRRB2DHQ/events.json","paper":"https://pith.science/paper/WTPC5YYK"},"agent_actions":{"view_html":"https://pith.science/pith/WTPC5YYKPQX5ADP3ANYRRB2DHQ","download_json":"https://pith.science/pith/WTPC5YYKPQX5ADP3ANYRRB2DHQ.json","view_paper":"https://pith.science/paper/WTPC5YYK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1602.06780&json=true","fetch_graph":"https://pith.science/api/pith-number/WTPC5YYKPQX5ADP3ANYRRB2DHQ/graph.json","fetch_events":"https://pith.science/api/pith-number/WTPC5YYKPQX5ADP3ANYRRB2DHQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WTPC5YYKPQX5ADP3ANYRRB2DHQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WTPC5YYKPQX5ADP3ANYRRB2DHQ/action/storage_attestation","attest_author":"https://pith.science/pith/WTPC5YYKPQX5ADP3ANYRRB2DHQ/action/author_attestation","sign_citation":"https://pith.science/pith/WTPC5YYKPQX5ADP3ANYRRB2DHQ/action/citation_signature","submit_replication":"https://pith.science/pith/WTPC5YYKPQX5ADP3ANYRRB2DHQ/action/replication_record"}},"created_at":"2026-05-18T01:16:54.473987+00:00","updated_at":"2026-05-18T01:16:54.473987+00:00"}